Conventional signal processing is performed on the basis of a Nyquist sampling theory, that is, a quantity of discrete samples required for reconstructing a signal without distortion is decided by a bandwidth of the signal. Specifically, when a sampling frequency is greater than twice a highest frequency in the signal, information in the original signal is integrally retained in a digital signal obtained after sampling.
In the radio communications field, a spectral bandwidth for transmitting a radio signal tends to increase. As the spectral bandwidth increases, a higher requirement is imposed on a sampling rate of an analog-to-digital converter (ADC). Design of a high-rate ADC increases complexity of terminal design, and is expensive. For example, aggregation of multiple spectral subbands and a dynamic change of a subband frequency have been widely applied to existing radio communications systems. However, an ADC in an existing terminal generally uses a subband sampling manner. That is, one frequency converter and one filter are used for each subband, and one frequency converter and one filter need to be added provided that one subband is added. Due to a limited size of a terminal, requirements of aggregation of multiple spectral subbands and a dynamic change of a subband frequency can be hardly met.
Compressive sampling is a new sampling theory. A signal sparseness characteristic is developed, so that under a condition under which a sampling rate is far less than a Nyquist sampling rate, a discrete sample of a signal is obtained by means of random sampling, and then distortionless reconstruction of the signal is implemented by using a nonlinear reconstruction algorithm. The compressive sampling theory has a low requirement for the sampling frequency, and therefore, has a broad application prospect.
Currently, many communications systems divide one wideband spectrum into multiple narrow bands, and different narrow bands are used to carry different narrowband signals. For example, in an OFDM system, a spectrum is divided into multiple subbands, multiple subbands occupied by one OFDM signal transmitted by a transmitter may be distributed apart in terms of frequencies, and the subbands occupied by the OFDM signal may vary with time dynamically. For this multi-band signal, before performing compressive sampling on a received analog signal, many compressive sampling receiving devices need to learn beforehand information about a frequency band occupied by a to-be-sampled frequency band signal. An MWC (Modulated Wideband Converter) system is proposed by persons such as Moshe Mishali (for details, refer to IEEE Journal of Selected Topics In Signal Processing, Vol. 4, No. 2, April 2010, entitled “From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signal”). The system has multiple sampling channels, and parallel processing is performed on a received signal on the multiple sampling channels. On each sampling channel, the received signal is first multiplied by a periodic pseudo random sequence (or called a frequency mixing function), a result of which is equivalent to shifting a part of a wideband spectrum to the vicinity of a baseband. The part of the wideband spectrum shifted by using the sampling channel depends on a specific form of the periodic pseudo random sequence, which is described in detail by Moshe Mishali in the foregoing document. Then a low-pass filter filters out a part except signals in the vicinity of the baseband, and the signals in the vicinity of the baseband are sampled by using a low-rate ADC whose sampling rate is far less than a Nyquist frequency. Different periodic pseudo random sequences (the periodic pseudo random sequences have a same period Tp) are set for different sampling channels, for the purpose of shifting an entire spectrum to a same frequency band near the baseband on a per fp=1/Tp basis. In this way, no matter which narrow bands are used by a transmit end to send radio signals, spectrums of the radio signals are all shifted to the frequency band near the baseband, and information in the multi-band signals can be restored subsequently by using a signal restoration algorithm.
However, the foregoing compressive sampling manner has the following problem: after frequency mixing is performed on multi-band signals (the signals are aliased to a same frequency band) by using multiple sampling channels of a compressive sampling receiving device, mutual interference exists between the signals. Consequently, a signal to interference plus noise ratio (SINR) of a received signal is low, and an effect of subsequent signal restoration is poor.